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Coset

In mathematics, specifically group theory, a subgroup H of a group G may be used to decompose the underlying set of G into disjoint, equal-size subsets called cosets. There are left cosets and right cosets. Cosets (both left and right) have the same number of elements (cardinality) as does H. Furthermore, H itself is both a left coset and a right coset.…

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Overview

Definition

Properties

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As orbits of a group action

History

An application from coding theory

Double cosets

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Coset

Nodes76
Edges75
Triples147
Avg. degree1.97
Density0.026316
Components1

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Coset

Top relations

related to References · 34
Coset → Abstract Algebra, Addison-Wesley, Applewood Books, Applications, Basic Algebra, Brown Publishers, Burton, Classical Abstract Algebra, Cosets, Courier Dover Publications, David, Discrete Mathematics, Dover, Finite Groups, First Course, Foundations, Group Theory, Groups, Harper, ISBN
related to history · 16
Coset → Applied Mathematics, Burnside, Camille Jordan, Galois, Galois's, German Nebengruppen, He, If, Mathematics, Miller, Note, Pure, Quarterly Journal, The, Various, Weber
related to External links · 13
Coset → EMS PressCoset, Encyclopedia, Eric, Illustrated, Ivanova, Left Coset, Mathematics, MathWorld, Nicolas Bray, PlanetMath, Right Coset, The Group Properties Wiki, Weisstein
related to An application from coding theory · 11
Coset → An, As, Codes, GF, Namely, Now, One, The, Then, This, When
related to Integers · 10
Coset → Abelian, Again, Due, Let, That, The, Then, There, These, This
has application · 9
Coset → Clifford, Cosets, For, In, Klein, Lie, Rubik's Cube, Thistlethwaite's, Vitali
related to Normal subgroups · 9
Coset → For, Furthermore, Ha, Hb, If, Ng, Some, That, This
related to Double cosets · 7
Coset → Given, HgK, HxK, HyK, The, These, Two
related to First example · 6
Coset → Cayley, In, Its, Let, The, This
related to Vectors · 6
Coset → Another, For, If, In, R2, The

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Important terminology

cosets group left right subgroup element normal elements example used called set vector isbn form every number double theory subgroups

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cosetis aleft coset0.90text
vector spacesinstance ofCosets also appear in other areas of mathematics0.80text
error-correcting codesinstance ofCosets also appear in other areas of mathematics0.80text
Cosethas applicationCosets0.60section
Cosethas applicationVitali0.60section
Cosethas applicationFor0.60section
Cosethas applicationThistlethwaite's0.60section
Cosethas applicationRubik's Cube0.60section
Cosethas applicationIn0.60section
Cosethas applicationClifford0.60section
Cosethas applicationKlein0.60section
Cosethas applicationLie0.60section

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